Don't store them. Hash the password and store that, using a suitably strong algorithm that's relatively chunky and expensive to compute en masse (most, if not all, modern options, such as scrypt, Argon2, and bcrypt, support a scaling work factor so that in the future you can increase the work needed as computing resources increase). Then you can compute a hash based on the password that's passed in and make sure that they match.

Some folks will then further encrypt the stored hashes such that a database compromise, but not an application-server compromise, leaves the attacker without the keys necessary to decrypt even the hashes, but I am ambivalent about the usefulness of that (can't hurt, but the threat model for that seems more geared towards internal threats than external).